Subs equalized outdoors for the same target response through the passband of 40-120 Hz using a DBX Driverack PA, Smaart Magnitude response, one a small bass reflex, the other a bandpass box.

I was the listener and builder of both cabinets.
I am sighted.

The exact curve of the frequency reponse particularly the roll off of the bottom end, that is the Q is what reflects the transient response...and to me seems very difficult to replicate by equalization in two different subs having different loading....unless very sophisticated means are used. Simmed or modelled FR curves might not be as close to real world radiated sound from the woofer.

Unless the Q and also the LF extension, after equalisation of the two differently loaded or not subs is exact, the subjective sound perception is bound to differ, due to differing Q of the system.

So you are saying that the Fourier transform is not valid? Because if it is then the two systems with identical FR with have identical transient response.

I never mentioned the Fourier transform being invalid, though perhaps you could elucidate your proposition that two different cabinet designs equalized for identical FR would have identical transient response.

One can equalize a Wurlitzer jukebox to have the same response as a sealed woofer, but they won't sound the same to my ears.
And obviously, a horn loaded woofer's transient would lag by the path length difference, though it's frequency response could easily be equalized the same as a sealed box.
Perhaps you are more sensitive to HOMs and I'm more sensitive to LF differences, to each his own .

Subs equalized outdoors for the same target response through the passband of 40-120 Hz using a DBX Driverack PA, Smaart Magnitude response, one a small bass reflex, the other a bandpass box.

I was the listener and builder of both cabinets.
I am sighted.

And then you put them in a room and listened A/B? Where did you place them in the room and where was the listening position (was it always exactly the same)? Did you also take in-room measurements at the listening position?

I can't say that I have, but I do get JAES and I usually read papers that interest me, but I skip those that look like "old news". What do they say?

They look at low frequency reproduction not only from the perspective of magnitude response but they also look at the influence of modal decay. There seems to be a modal decay threshold that greatly influences the perceived quality.
They also looked at different sub configurations and how they perform. The systems reducing modal decay (like CABS) performed best.

They look at low frequency reproduction not only from the perspective of magnitude response but they also look at the influence of modal decay. There seems to be a modal decay threshold that greatly influences the perceived quality.
They also looked at different sub configurations and how they perform. The systems reducing modal decay (like CABS) performed best.

I find those papers pretty interesting. Unfortunately, they did not include any gradient woofer system in their tests like a dipole or cardio. Since they excite less modes and to a different degree, there is less energy in the room to decay to begin with. That doesn't change the decay properties of the room but the threshold is potentially reached faster.
Here is the link to the abstract:

I find those papers pretty interesting. Unfortunately, they did not include any gradient woofer system in their tests like a dipole or cardio. Since they excite less modes and to a different degree, there is less energy in the room to decay to begin with. That doesn't change the decay properties of the room but the threshold is potentially reached faster.

I partly agree.

The problem with dipoles is their very, very low efficiency below Fequal. How to get 20Hz or even 10Hz at movie reference level (115dB SPL) out of a dipole?